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The Shift-Moebius transform of [1,2,3,4,...].
3

%I #5 Mar 30 2012 18:37:44

%S 1,1,1,1,1,0,1,0,-1,-2,0,-3,0,-5,-6,-4,-2,-7,-3,-8,-7,-6,-4,-9,-5,-9,

%T -10,-9,-2,-9,3,-2,-4,-4,-7,-2,9,2,-7,2,9,5,14,10,7,21,20,20,28,21,20,

%U 28,35,31,28,44,45,56,50,53,65,62,37,61,54,66,69,71,59,75,83,93,97,92,60,87,74,99,95,106,98,117,104,102

%N The Shift-Moebius transform of [1,2,3,4,...].

%C See triangle A117165 for the definition of the Shift-Moebius transform.

%F a(n) = Sum_{k=1,n} A117165(n,k)*k.

%o (PARI) {a(n)=sum(k=1,n,prod(i=0,n, matrix(n,n,r,c,if(r>=c,if((r+n-i)%(c+n-i)==0,moebius((r+n-i)/(c+n-i)),0))))[ n,k]*k)}

%Y Cf. A117165, A117176.

%K sign

%O 1,10

%A _Wouter Meeussen_ and _Paul D. Hanna_, Mar 05 2006